__src_index__ int64 0 172k | messages stringlengths 375 66.5k |
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1,544 | [{"role": "user", "content": "Compute $(142 + 29 + 26 + 14) \\times 2$."}, {"role": "assistant", "content": "<think>\n\nOkay, let's see. I need to compute (142 + 29 + 26 + 14) multiplied by 2. Hmm, first, maybe I should add up all the numbers inside the parentheses first, and then multiply the result by 2. Let me start... |
1,401 | [{"role": "user", "content": "There is a cage with 10 cats, including 7 white cats and 3 black cats. The cage door is opened slightly, allowing only one cat to exit at a time. The cats rush out one by one. If all 10 cats exit the cage, let \\( X \\) represent the number of segments into which the 7 white cats are divid... |
1,550 | [{"role": "user", "content": "After violating the group's policies, 20 members of a Facebook group were removed by the group's admin. If each member posted 50 messages per day in the group and the number of members in the group was 150 before the admin removed some, calculate the total number of messages the remaining ... |
1,461 | [{"role": "user", "content": "From 1812 identical squares with a side length of 1 mm, a rectangular frame was made for a group photo. The boundaries of the photo coincide with the inner boundaries of the frame. Then the photo was cut along the millimeter grid line into two rectangular parts. Now, two frames were needed... |
1,546 | [{"role": "user", "content": "In triangle $ABC$, sides $AB$ and $AC$ are $5$ inches and $8$ inches long, respectively. The median $AD$ from vertex $A$ to the midpoint of side $BC$ is $4.5$ inches. Calculate the length of side $BC$.\nA) $\\sqrt{89}$ inches\nB) $\\sqrt{92}$ inches\nC) $\\sqrt{97}$ inches\nD) $\\sqrt{101}... |
1,514 | [{"role": "user", "content": "Given that the line $ax + 2by - 2 = 0 (a, b > 0)$ always bisects the circumference of the circle ${x^{2}} + {y^{2}} - 4x - 2y - 8 = 0$, find the minimum value of $\\frac{1}{a} + \\frac{2}{b}$ ( )."}, {"role": "assistant", "content": "<think>\n\nOkay, let's try to solve this problem step by... |
1,509 | [{"role": "user", "content": "There is a special calculator. When a number is input, the calculator will multiply the number by 2, then reverse the digits of the result. Finally, it will add 2 and display the final result. If you input a two-digit number and the final displayed result is 27, what was the initial input?... |
1,557 | [{"role": "user", "content": "Christopher uses 1 packet of a sugar substitute in his coffee. He has 2 coffees a day. The packets come 30 to a box and cost $4.00 a box. How much will it cost him to have enough sugar substitutes to last him 90 days?"}, {"role": "assistant", "content": "<think>\n\nOkay, let's see. Chri... |
1,558 | [{"role": "user", "content": "Joshua bought 25 oranges for a certain amount. If he sells each one for 60c and makes a profit of 10 cents on each orange, how much did he spend on buying the oranges?"}, {"role": "assistant", "content": "<think>\n\nOkay, let's see. The problem is about Joshua buying oranges and selling th... |
1,486 | [{"role": "user", "content": "The height of a triangle, equal to 2 cm, divides the angle of the triangle in the ratio 2:1 and the base of the triangle into parts, where the smaller part is 1 cm. Determine the area of the triangle."}, {"role": "assistant", "content": "<think>\n\nThis is a complex or challenging question... |
1,506 | [{"role": "user", "content": "Let \\( x \\) and \\( y \\) be complex numbers such that\n\\[\n\\frac{x^3 + y^3}{x^3 - y^3} + \\frac{x^3 - y^3}{x^3 + y^3} = 1.\n\\]\nFind\n\\[\n\\frac{x^6 + y^6}{x^6 - y^6} + \\frac{x^6 - y^6}{x^6 + y^6}.\n\\]"}, {"role": "assistant", "content": "<think>\n\nThis is a complex or challengin... |
1,487 | [{"role": "user", "content": "Circle $A$ is tangent to Circle $B$, with Circle $B$ passing through the center of Circle $A$. The area of Circle $A$ is 16 square inches. Calculate the area of Circle $B$, in square inches.\n$\\textbf{(A) } 2\\qquad \\textbf{(B) } 4\\qquad \\textbf{(C) } 8\\qquad \\textbf{(D) } 16\\qquad ... |
1,560 | [{"role": "user", "content": "if ( 5 + k ) ( 5 - k ) = ( 5 ^ 2 ) - ( 2 ^ 3 ) , then what is the value of k ?"}, {"role": "assistant", "content": "<think>\n\nOkay, let's see. The problem is: if (5 + k)(5 - k) equals 5 squared minus 2 cubed, then what's the value of k? Hmm, first, I need to remember some algebraic identi... |
1,529 | [{"role": "user", "content": "Given two straight lines $l_1: 2x - y = 0$ and $l_2: x + y + 2 = 0$.\n(1) Find the equation of the straight line $l$ that passes through point $P(1, 1)$ and is perpendicular to $l_1$.\n(2) If the center of the circle $M$ lies on $l_1$, the circle is tangent to the $y$-axis, and the chord l... |
1,513 | [{"role": "user", "content": "How many solutions does the equation\n\n\\[ x^{2}+y^{2}+2xy-1988x-1988y=1989 \\]\n\nhave in the set of positive integers?"}, {"role": "assistant", "content": "<think>\n\nThis is a complex or challenging question, and it is difficult to provide a direct and correct answer. I need to think a... |
1,495 | [{"role": "user", "content": "Let $a,$ $b,$ $c$ be real numbers such that $9a^2 + 4b^2 + 25c^2 = 1.$ Find the maximum value of\n\\[8a + 3b + 5c.\\]"}, {"role": "assistant", "content": "<think>\n\nThis is a complex or challenging question, and it is difficult to provide a direct and correct answer. I need to think about... |
1,527 | [{"role": "user", "content": "The point $O$ is the center of the circle circumscribed about $\\triangle ABC$, with $\\angle BOC = 140^{\\circ}$ and $\\angle AOB = 130^{\\circ}$. Determine the degree measure of $\\angle ABC$."}, {"role": "assistant", "content": "<think>\n\nThis is a complex or challenging question, and ... |
1,483 | [{"role": "user", "content": "Simplify the expression \\[(x+y+z)^{2010} + (x-y-z)^{2010}\\] by expanding it and combining like terms. How many terms are in the simplified expression?"}, {"role": "assistant", "content": "<think>\n\nThis is a complex or challenging question, and it is difficult to provide a direct and co... |
1,442 | [{"role": "user", "content": "\nIn triangle \\(ABC\\), points \\(M\\) and \\(N\\) are the midpoints of sides \\(AC\\) and \\(AB\\) respectively. On the median \\(BM\\), a point \\(P\\) is chosen such that it does not lie on line \\(CN\\). It turns out that \\(PC = 2PN\\). Prove that \\(AP = BC\\)."}, {"role": "assistan... |
1,537 | [{"role": "user", "content": "In the entrance examination for the 2015 class at Nanshan Middle School Experimental School, a total of 60 examination rooms were set up, with room numbers ranging from 001 to 060. Now, using systematic sampling, 12 examination rooms are selected for inspection. Room 007 has already been i... |
1,435 | [{"role": "user", "content": "For a function $f(x)$ defined on domain $D$, if there exist two lines $y=kx+m_1$ and $y=kx+m_2$ with a distance of $d$ between them, such that for any $x \\in D$, the inequality $kx+m_1 \\leqslant f(x) \\leqslant kx+m_2$ holds, then the function $f(x)$ ($x \\in D$) is said to have a channe... |
1,515 | [{"role": "user", "content": "In triangle $ABC$ such that $\\angle ACB=90^{\\circ}$ , let point $H$ be foot of perpendicular from point $C$ to side $AB$ . Show that sum of radiuses of incircles of $ABC$ , $BCH$ and $ACH$ is $CH$ "}, {"role": "assistant", "content": "<think>\n\nThis is a complex or challen... |
1,556 | [{"role": "user", "content": "Given that line $l$ intersects with line $y=2$ and $x-y-1=0$ at points A and B, respectively, and the midpoint of segment AB is (2, -1), find the slope of line $l$."}, {"role": "assistant", "content": "<think>\n\nThis is a complex or challenging question, and it is difficult to provide a d... |
1,576 | [{"role": "user", "content": "Calculate $\\sqrt{50} + \\sqrt{32} + \\sqrt{24}$.\nA) $9\\sqrt{2} + 2\\sqrt{6}$ \nB) $11\\sqrt{2}$ \nC) $7\\sqrt{2} + 2\\sqrt{6}$ \nD) $13\\sqrt{2}$"}, {"role": "assistant", "content": "<think>\n\nOkay, let's see. I need to calculate the sum of three square roots: √50 + √32 + √24. Hmm, ... |
1,508 | [{"role": "user", "content": "Given \\( a, b, c > 0 \\), show that\n\n\\[ \n\\frac{3}{a^{3} + b^{3} + c^{3}} \\leq \\frac{1}{a^{3} + b^{3} + abc} + \\frac{1}{b^{3} + c^{3} + abc} + \\frac{1}{c^{3} + a^{3} + abc} \\leq \\frac{1}{abc} \n\\]"}, {"role": "assistant", "content": "<think>\n\nThis is a complex or challenging ... |
1,578 | [{"role": "user", "content": "If $\\sqrt{4+2x}$ is meaningful within the real number range, then the range of $x$ is ____."}, {"role": "assistant", "content": "<think>\n\nOkay, let's see. The problem is asking for the range of x such that the square root of (4 + 2x) is meaningful in the real number range. Hmm, right. S... |
1,499 | [{"role": "user", "content": "When the digits in the number $2005$ are reversed we obtain the number $5002,$ and $5002 = a \\cdot b \\cdot c$, such that $a$, $b$ and $c$ are three distinct primes. How many other positive integers are the products of exactly three distinct primes $p_1$, $p_2$ and $p_3$ such that $p_1 + ... |
1,552 | [{"role": "user", "content": "How many positive integers less than 60 have an even number of positive divisors?"}, {"role": "assistant", "content": "<think>\n\nThis is a complex or challenging question, and it is difficult to provide a direct and correct answer. I need to think about it.\nWell, so the problem is asking... |
1,572 | [{"role": "user", "content": "If $a^x = 2$ and $a^y = 3$, then $a^{2x+3y} =$ ?"}, {"role": "assistant", "content": "<think>\n\nOkay, let's see. The problem says that \\( a^x = 2 \\) and \\( a^y = 3 \\), and we need to find \\( a^{2x + 3y} \\). Hmm, I remember that when dealing with exponents, there are some rules about... |
1,471 | [{"role": "user", "content": "If \\( x + \\frac{1}{y} = 2 \\) and \\( y + \\frac{1}{z} = 1 \\), what is the value of the product \\( xyz \\)?"}, {"role": "assistant", "content": "<think>\n\nOkay, let's see. I need to find the value of the product \\( xyz \\) given the equations \\( x + \\frac{1}{y} = 2 \\) and \\( y + ... |
1,535 | [{"role": "user", "content": "If $2^{a}+\\log _{2}a=4^{b}+2\\log _{4}b$, then ()\n\nA: $a \\gt 2b$\n\nB: $a \\lt 2b$\n\nC: $a \\gt b^{2}$\n\nD: $a \\lt b^{2}$"}, {"role": "assistant", "content": "<think>\n\nOkay, let's try to solve this problem. The question is: If \\(2^{a} + \\log_{2}a = 4^{b} + 2\\log_{4}b\\), then w... |
1,583 | [{"role": "user", "content": "John with his five friends ordered 3 pizzas. Each pizza had a certain number of slices. They all finished and ate the same amount of pizzas, and each person ate 4 slices. How many slices did each pizza have?"}, {"role": "assistant", "content": "<think>\n\nOkay, let's try to figure out this... |
1,554 | [{"role": "user", "content": "Abby, Bridget, and seven of their classmates are arranged to sit in a three rows of three for a group photo:\n\\begin{eqnarray*} \n\\text{X}&\\quad\\text{X}\\quad&\\text{X} \\\\\n\\text{X}&\\quad\\text{X}\\quad&\\text{X} \\\\\n\\text{X}&\\quad\\text{X}\\quad&\\text{X}\n\\end{eqnarray*}\nIf... |
1,566 | [{"role": "user", "content": "Oil cans X and Y are right circular cylinders. The height and radius of Y are each some times those of X. If the oil in can X filled to capacity sells for $2, the oil in Y sells for $64 when Y is only half filled. What is the ratio of the height and radius of Y to those of X?"}, {"role": "... |
1,452 | [{"role": "user", "content": "The number 5.6 may be expressed uniquely (ignoring order) as a product \\( \\underline{a} \\cdot \\underline{b} \\times \\underline{c} . \\underline{d} \\) for digits \\( a, b, c, d \\) all nonzero. Compute \\( \\underline{a} . \\underline{b} + \\underline{c} . \\underline{d} \\)."}, {"rol... |
1,518 | [{"role": "user", "content": "Given a sequence of positive integers $$ a_1, a_2, a_3, a_4, a_5, \\dots $$ such that $a_2 > a_1$ and $a_{n+2} = 3a_{n+1} - 2a_n$ for all $n \\geq 1$ .\nProve that $a_{2021} > 2^{2019}$ ."}, {"role": "assistant", "content": "<think>\n\nThis is a complex or challenging question, and... |
1,551 | [{"role": "user", "content": "Let $f(x) = x^2 - 5x + 12$ and let $g(f(x)) = 3x + 4$. What is the sum of all possible values of $g(9)$?"}, {"role": "assistant", "content": "<think>\n\nThis is a complex or challenging question, and it is difficult to provide a direct and correct answer. I need to think about it.\nWell, s... |
1,577 | [{"role": "user", "content": "The zero point interval of the function $f(x)= \\frac {6}{x}-\\log _{2}x$ is $(\\quad)$ \nA: $(0,1)$ \nB: $(1,2)$ \nC: $(3,4)$ \nD: $(4,+\\infty)$"}, {"role": "assistant", "content": "<think>\n\nOkay, let's see. I need to find the zero point interval of the function \\( f(x) = \\frac{6... |
1,591 | [{"role": "user", "content": "The pressure \\( P \\) on a roof varies jointly as the area \\( A \\) of the roof and the square of the velocity \\( V \\) of the wind. There is a pressure of 2 pounds on a square meter when the wind velocity is 20 miles per hour. Find the velocity of the wind when the pressure on 4 square... |
1,585 | [{"role": "user", "content": "The range of the function $f(x) = 2x - x^2$ ($1 < x < 3$) is\n\nA: $\\mathbb{R}$ \nB: $[-3, +\\infty)$ \nC: $[-3, 1]$ \nD: $(-3, 1)$"}, {"role": "assistant", "content": "<think>\n\nOkay, let's see. I need to find the range of the function \\( f(x) = 2x - x^2 \\) where \\( 1 < x < 3 \\).... |
1,594 | [{"role": "user", "content": "Chris mixed 3 pounds of raisins with 3 pounds of nuts. If a pound of nuts costs a certain multiple of the cost of a pound of raisins, then the total cost of the raisins was 0.25 of the total cost of the mixture. What is the ratio of the cost of a pound of nuts to the cost of a pound of rai... |
1,586 | [{"role": "user", "content": "Given that the normal vectors of planes $\\alpha$ and $\\beta$ are $\\overrightarrow{m} = (1, -5, 2)$ and $\\overrightarrow{n} = (-3, 1, 4)$ respectively, then ( )\nA: $\\alpha \\perp \\beta$\nB: $\\alpha \\parallel \\beta$\nC: $\\alpha$ and $\\beta$ intersect but are not perpendicular\nD... |
1,588 | [{"role": "user", "content": "Calculate: ${(-2)^2}+\\sqrt{8}-|1-\\sqrt{2}|+{(2023-\\pi)^0}$."}, {"role": "assistant", "content": "<think>\n\nOkay, let's see. I need to calculate this expression: (-2) squared plus the square root of 8 minus the absolute value of (1 minus the square root of 2) plus (2023 minus pi) to the... |
1,534 | [{"role": "user", "content": "Let $D$ be the determinant of the matrix whose column vectors are $\\mathbf{a},$ $\\mathbf{b},$ and $\\mathbf{c}.$ Find the determinant of the matrix whose column vectors are $2\\mathbf{a} + \\mathbf{b},$ $\\mathbf{b} + \\mathbf{c},$ and $\\mathbf{c} + \\mathbf{a},$ in terms of $D.$"}, {"r... |
1,542 | [{"role": "user", "content": "Given that the center of ellipse $C$ is at the origin, the foci are on the $x$-axis, the length of the major axis is $2\\sqrt{3}$, and the eccentricity is $\\frac{\\sqrt{6}}{3}$. \n$(Ⅰ)$ Find the standard equation of ellipse $C$. \n$(Ⅱ)$ If the line $l$ passing through the point $(1,0)$ ... |
1,603 | [{"role": "user", "content": "Maria's birthday is in 22 days. Her friend Lilly wants to buy her flowers so she saves $2 each day until Maria's birthday. If a flower costs $4, how many flowers can Lilly buy?"}, {"role": "assistant", "content": "<think>\n\nOkay, let's see. Maria's birthday is in 22 days, and Lilly saves ... |
1,545 | [{"role": "user", "content": "In the plane rectangular coordinate system $xOy$, the parameter equation of the line $l$ is $\\left\\{\\begin{array}{l}x=-t\\\\ y=\\sqrt{3}-t\\end{array}\\right.$ ($t$ is the parameter). Taking $O$ as the pole and the positive half-axis of the $x$-axis as the polar axis, the polar coordina... |
1,517 | [{"role": "user", "content": "Two adjacent angles of a quadrilateral sum to $180^{\\circ}$. Prove that two of its sides are parallel. Prove that the other two angles also sum to $180^{\\circ}$."}, {"role": "assistant", "content": "<think>\n\nThis is a complex or challenging question, and it is difficult to provide a di... |
1,501 | [{"role": "user", "content": "There are 80 cable cars traveling in a circular route between ski resorts A and B, all moving in the same direction. The distance between two adjacent cable cars is the same. Xiaoming, who is sitting in one of the cable cars, encounters an opposing cable car every 15 seconds. How long does... |
1,601 | [{"role": "user", "content": "If the plane vectors $ \\overrightarrow{a}=(\\cos \\theta,\\sin \\theta)$ and $ \\overrightarrow{b}=(1,-1)$, and $ \\overrightarrow{a} \\perp \\overrightarrow{b}$, then the value of $\\sin 2\\theta$ is ______."}, {"role": "assistant", "content": "<think>\n\nOkay, let's see. The problem say... |
1,600 | [{"role": "user", "content": "What amazing conclusion can be drawn from the answer: \"There is something instead of nothing\"?"}, {"role": "assistant", "content": "<think>\n\nOkay, the user is asking about the amazing conclusion from the answer \"There is something instead of nothing.\" Hmm, this seems philosophical. L... |
1,485 | [{"role": "user", "content": "How many solutions for different values of \\( a \\) does the equation \\( x \\cdot |x - a| = a \\) have?"}, {"role": "assistant", "content": "<think>\n\nThis is a complex or challenging question, and it is difficult to provide a direct and correct answer. I need to think about it.\nWell, ... |
1,547 | [{"role": "user", "content": "Given \\( \\sin x + \\sin y = \\frac{1}{3} \\), find the maximum and minimum values of \\( \\sin x - \\cos^2 y \\)."}, {"role": "assistant", "content": "<think>\n\nThis is a complex or challenging question, and it is difficult to provide a direct and correct answer. I need to think about i... |
1,575 | [{"role": "user", "content": "Given that $a > 0$ and $b > 0$, the function $f(x) = |x-a| + |x+b|$ has a minimum value of $2$. \n$(1)$ Find the value of $a+b$; \n$(2)$ Prove that it is not possible for both $a^{2}+a > 2$ and $b^{2}+b > 2$ to hold at the same time."}, {"role": "assistant", "content": "<think>\n\nThis i... |
1,493 | [{"role": "user", "content": "If $f(x)$ is a function defined only for $0 \\le x \\le 1$, and $f(x) = ax^2 + bx + c$ for constants $a$, $b$, and $c$ where $a < 0$, then what is the range of $f$ in terms of $a$, $b$, and $c$? Express your answer in interval notation."}, {"role": "assistant", "content": "<think>\n\nThis ... |
1,605 | [{"role": "user", "content": "Which type of conic section is described by the equation \\[\\sqrt{x^2 + (y-2)^2} + \\sqrt{(x-6)^2 + (y+4)^2} = 14?\\] Enter \"C\" for circle, \"P\" for parabola, \"E\" for ellipse, \"H\" for hyperbola, and \"N\" for none of the above."}, {"role": "assistant", "content": "<think>\n\nOkay, ... |
1,567 | [{"role": "user", "content": "Find the integer \\(n\\), \\(0 \\le n \\le 360\\), such that \\(\\cos n^\\circ = \\cos 340^\\circ.\\)"}, {"role": "assistant", "content": "<think>\n\nThis is a complex or challenging question, and it is difficult to provide a direct and correct answer. I need to think about it.\nWell, so I... |
1,524 | [{"role": "user", "content": "The number of solutions of \\( 2^{2x} - 3^{2y} = 80 \\), in which \\( x \\) and \\( y \\) are integers, is:\n\\[\\textbf{(A)} \\ 0 \\qquad\\textbf{(B)} \\ 1 \\qquad \\textbf{(C)} \\ 2 \\qquad\\textbf{(D)} \\ 3\\qquad \\textbf{(E)} \\ \\text{More than three, but finite}\\]"}, {"role": "assi... |
1,584 | [{"role": "user", "content": "Given real numbers $a$, $b$, $c$ satisfy: $a=3^{\\frac{1}{4}}-3^{-\\frac{1}{4}}$, $b=\\frac{1}{2}\\ln 3$, $c=4-2\\sqrt{3}$, then ()\n\nA: $a \\gt b \\gt c$\n\nB: $b \\gt c \\gt a$\n\nC: $b \\gt a \\gt c$\n\nD: $c \\gt a \\gt b$"}, {"role": "assistant", "content": "<think>\n\nOkay, let's tr... |
1,561 | [{"role": "user", "content": "The three-digit positive integer $N$ has a ones digit of 7. What is the probability that $N$ is divisible by 4? Express your answer as a common fraction."}, {"role": "assistant", "content": "<think>\n\nThis is a complex or challenging question, and it is difficult to provide a direct and c... |
1,604 | [{"role": "user", "content": "Simplify the expression $\\sqrt{1-2\\sin 1\\cos 1}$. The result is ($\\quad\\quad$).\nA: $\\sin 1-\\cos 1$\nB: $\\cos 1-\\sin 1$\nC: $\\sin 1+\\cos 1$\nD: $-\\sin 1-\\cos 1$"}, {"role": "assistant", "content": "<think>\n\nOkay, let's see. I need to simplify the expression √(1 - 2 sin 1 cos... |
1,570 | [{"role": "user", "content": "Andrea is three times as old as Jim was when Jim was twice as old as he was when the sum of their ages was $47$ . If Andrea is $29$ years older than Jim, what is the sum of their ages now?"}, {"role": "assistant", "content": "<think>\n\nThis is a complex or challenging question, and it ... |
1,612 | [{"role": "user", "content": "there are 720 male and female participants in a meeting . half the female participants and one - quarterof the male participants are democrats . one - third of all the participants are democrats . how many of the democrats are female ?"}, {"role": "assistant", "content": "<think>\n\nOkay, ... |
1,538 | [{"role": "user", "content": "For how many real numbers $b$ does the quadratic equation $x^2 + bx + 10b = 0$ have only integer roots for $x$?"}, {"role": "assistant", "content": "<think>\n\nThis is a complex or challenging question, and it is difficult to provide a direct and correct answer. I need to think about it.\n... |
1,597 | [{"role": "user", "content": "In the updated game of Frood, dropping $n$ froods still gives a score of $\\frac{n(n+1)}{2}$ points. However, eating $n$ froods now earns $15n$ points. What is the least number of froods for which dropping them will earn more points than eating them?"}, {"role": "assistant", "content": "<t... |
1,618 | [{"role": "user", "content": "Given the complex number $z=-\\frac{1}{2}+\\frac{\\sqrt{3}}{2}i$, find $\\overline{z}+|z|=$ ( ),\n\nA: $-\\frac{1}{2}-\\frac{\\sqrt{3}}{2}i$\nB: $-\\frac{1}{2}+\\frac{\\sqrt{3}}{2}i$\nC: $\\frac{1}{2}+\\frac{\\sqrt{3}}{2}i$\nD: $\\frac{1}{2}-\\frac{\\sqrt{3}}{2}i$"}, {"role": "assistant", ... |
1,613 | [{"role": "user", "content": "Proposition p: $\\{2\\} \\in \\{1, 2, 3\\}$, proposition q: $\\{2\\} \\subseteq \\{1, 2, 3\\}$. Among the following judgments: ① p or q is true; ② p or q is false; ③ p and q are true; ④ p and q are false; ⑤ not p is true; ⑥ not q is false. The number of correct judgments is ( )\nA: 2\nB: 3... |
1,611 | [{"role": "user", "content": "If line $l$ passes through the point $(2, -1)$ and is perpendicular to the line $x-2y+1=0$, then the equation of line $l$ is."}, {"role": "assistant", "content": "<think>\n\nOkay, let's see. I need to find the equation of a line l that passes through the point (2, -1) and is perpendicular ... |
1,592 | [{"role": "user", "content": "Given two non-coincident lines $m$ and $n$, and two different planes $\\alpha$ and $\\beta$, which of the following statements is correct?\n\nA: If $m \\parallel \\alpha$, $n \\parallel \\beta$, and $m \\parallel n$, then $\\alpha \\parallel \\beta$.\n\nB: If $m \\perp \\alpha$, $n \\paral... |
1,626 | [{"role": "user", "content": "Given the function $f(x) = \\frac{\\ln x}{x}$, and $f'(x)$ is the derivative of $f(x)$, then the value of $f'(1)$ is ______."}, {"role": "assistant", "content": "<think>\n\nOkay, let's see. I need to find the value of f'(1) where f(x) is ln x divided by x. First, I remember that to find th... |
1,622 | [{"role": "user", "content": "If set $A = \\{1, m^2\\}$, and $B = \\{2, 4\\}$, then \"m=2\" is the ( ) condition for \"$A \\cap B = \\{4\\}$\".\nA: Necessary and sufficient condition\nB: Necessary but not sufficient condition\nC: Sufficient but not necessary condition\nD: Neither sufficient nor necessary condition"}, {... |
1,587 | [{"role": "user", "content": "A community plans to invest $500$ yuan to purchase three types of books, $A$, $B$, and $C, to enrich the cultural life of the residents and create a \"bookish community.\" Type $A$ costs $30$ yuan per book, type $B$ costs $25$ yuan per book, and type $C$ costs $20$ yuan per book. The commu... |
1,553 | [{"role": "user", "content": "The digits from 1 to 9 are each written on nine separate pieces of paper and placed in a hat. Jack randomly selects one piece of paper and then returns it to the hat. Jill then randomly selects one piece of paper. What is the most likely units digit of the sum of the numbers selected by Ja... |
1,523 | [{"role": "user", "content": "Several classmates together ate a cake. Alex ate the most, $\\frac{1}{11}$ of the entire cake, and Alena ate the least, $\\frac{1}{14}$ of the entire cake. How many classmates ate the cake? List all possible options."}, {"role": "assistant", "content": "<think>\n\nThis is a complex or chal... |
1,630 | [{"role": "user", "content": "If some men take 15 days to complete a job, then 18 men can finish that work in 20 days. How many men were initially working on the job?"}, {"role": "assistant", "content": "<think>\n\nOkay, let's try to figure out this problem. So, the question says: If some men take 15 days to complete a... |
1,629 | [{"role": "user", "content": "A person wants to give his money of $5400 to his 3 children a, b, c. B's share is $1800. What is the ratio of the shares for children a, b, and c?"}, {"role": "assistant", "content": "<think>\n\nOkay, let's see. The problem says a person wants to give $5400 to his 3 children a, b, c. B's s... |
1,621 | [{"role": "user", "content": "Let $S_{n}$ be the sum of the first $n$ terms of a geometric sequence $\\{a_{n}\\}$. If $8S_{6}=7S_{3}$, then the common ratio of $\\{a_{n}\\}$ is ______."}, {"role": "assistant", "content": "<think>\n\nOkay, let's see. The problem says that for a geometric sequence {a_n}, the sum of the f... |
1,564 | [{"role": "user", "content": "Given an arithmetic sequence $\\{a_{n}\\}$ with a common difference of $\\frac{{2π}}{3}$, let $S=\\{\\cos a_{n}|n\\in N^{*}\\}$. If $S=\\{a,b\\}$, then $ab=\\left(\\ \\ \\right)$\n\nA: $-1$\n\nB: $-\\frac{1}{2}$\n\nC: $0$\n\nD: $\\frac{1}{2}$"}, {"role": "assistant", "content": "<think>\n\... |
1,643 | [{"role": "user", "content": "In a football game, wristbands were given to every spectator for both their hands. In total 234 wristbands were distributed. How many people watched the game?"}, {"role": "assistant", "content": "<think>\n\nOkay, let's see. The problem says that in a football game, wristbands were given to... |
1,598 | [{"role": "user", "content": "A right pyramid has a square base with perimeter 32 inches. Its apex is 12 inches from each of the other vertices. What is the height of the pyramid from its peak to the center of its square base, in inches?"}, {"role": "assistant", "content": "<think>\n\nThis is a complex or challenging q... |
1,511 | [{"role": "user", "content": "Given that the center of circle C is at the origin O, and it is tangent to line $l\\_1: x - y - 2\\sqrt{2} = 0$.\n(1) If a line perpendicular to line $l\\_1$ intersects circle C at two distinct points P and Q, and a circle passing through the origin with PQ as the diameter, find the y-inte... |
1,581 | [{"role": "user", "content": "The negation of the proposition \"If $x > 2015$, then $x > 0$\" is ( ).\n\nA: If $x > 2015$, then $x \\leq 0$\nB: If $x \\leq 0$, then $x \\leq 2015$\nC: If $x \\leq 2015$, then $x \\leq 0$\nD: If $x > 0$, then $x > 2015$"}, {"role": "assistant", "content": "<think>\n\nOkay, let's see. The... |
1,602 | [{"role": "user", "content": "Let $f(x) = 2\\sqrt{x} + \\frac{12}{\\sqrt{x}}$ and let $g(x) = 3x^2 - 5x - 4$. What is $f(g(4))$?"}, {"role": "assistant", "content": "<think>\n\nThis is a complex or challenging question, and it is difficult to provide a direct and correct answer. I need to think about it.\nWell, so I ne... |
1,642 | [{"role": "user", "content": "In a Math competition, Sammy scored 20 points, Gab scored twice as many as Sammy's score, while Cher scored twice as many as Gab's score. They have 55 more points than their opponent. How many points did their opponent score?"}, {"role": "assistant", "content": "<think>\n\nOkay, let's try ... |
1,607 | [{"role": "user", "content": "Express $2.\\overline{06}$ as a reduced fraction, given that $0.\\overline{01}$ is $\\frac{1}{99}$."}, {"role": "assistant", "content": "<think>\n\nThis is a complex or challenging question, and it is difficult to provide a direct and correct answer. I need to think about it.\nWell, so I n... |
1,634 | [{"role": "user", "content": "Simplify the polynomial $\\{(2x+1)^{5}-5(2x+1)^{4}+10(2x+1)^{3}-10(2x+1)^{2}+5(2x+1)-1\\}$. The result is $\\(\\quad\\)$.\n\nA: $\\((2x+2)^{5}\\)$\nB: $2x^{5}$\nC: $\\((2x-1)^{5}\\)$\nD: $32x^{5}$"}, {"role": "assistant", "content": "<think>\n\nOkay, let's see. I need to simplify this poly... |
1,641 | [{"role": "user", "content": "Find the domain of the function\n\\[ g(x) = \\frac{x^2 + 4x - 7}{\\sqrt{6 - x}}. \\]"}, {"role": "assistant", "content": "<think>\n\nOkay, let's see. I need to find the domain of the function \\( g(x) = \\frac{x^2 + 4x - 7}{\\sqrt{6 - x}} \\). Hmm, domain means all the x-values that make t... |
1,548 | [{"role": "user", "content": "Prove that if the square of a $k$-digit number starts with the same $k$ digits, then this number is a power of 10."}, {"role": "assistant", "content": "<think>\n\nThis is a complex or challenging question, and it is difficult to provide a direct and correct answer. I need to think about it... |
1,627 | [{"role": "user", "content": "Find the positive real number $x$ such that $\\displaystyle \\frac{x-6}{11} = \\frac{6}{x-11}$."}, {"role": "assistant", "content": "<think>\n\nThis is a complex or challenging question, and it is difficult to provide a direct and correct answer. I need to think about it.\nWell, so I need ... |
1,658 | [{"role": "user", "content": "Melanie had 7 dimes in her bank. Her dad gave her some dimes and her mother gave her 4 dimes. Now, Melanie has 19 dimes. How many dimes did her dad give her?"}, {"role": "assistant", "content": "<think>\n\nOkay, let's see. Melanie started with 7 dimes. Then her dad gave her some dimes, and... |
1,633 | [{"role": "user", "content": "Find\n\\[\\sin \\left( \\sin^{-1} \\frac{4}{5} + \\tan^{-1} \\frac{1}{2} \\right).\\]"}, {"role": "assistant", "content": "<think>\n\nOkay, let's see. I need to find the sine of the sum of two inverse trigonometric functions: arcsin(4/5) and arctan(1/2). Hmm, right. So, the problem is sin(... |
1,650 | [{"role": "user", "content": "A certain volume of water is in a container of sphere. To transfer all the water into small hemispheres of volume 4 l each, 2734 hemisphere containers are required. What is the total volume of water in the sphere container?"}, {"role": "assistant", "content": "<think>\n\nOkay, let's try to... |
1,648 | [{"role": "user", "content": "The point corresponding to the complex number $z= \\frac {2-i}{1+i}$ is located in the \\_\\_\\_\\_\\_ quadrant of the complex plane."}, {"role": "assistant", "content": "<think>\n\nOkay, let's see. I need to figure out which quadrant the complex number \\( z = \\frac{2 - i}{1 + i} \\) is ... |
1,616 | [{"role": "user", "content": "Which of the following statements is correct?\n\nA: A necessary but not sufficient condition for the inequality $mx^{2}+x+m \\gt 0$ to hold for all $x \\in \\mathbb{R}$ is $m \\gt \\frac{1}{4}$.\n\nB: For $x, y \\in \\mathbb{R}$, the inequality $x^{2}+y^{2}\\geqslant 4$ is a sufficient but... |
1,590 | [{"role": "user", "content": "Find the limits:\n1) \\(\\lim_{x \\rightarrow 2}\\left(3x^{2}-2x+7\\right)\\)\n2) \\(\\lim_{x \\rightarrow 3} \\frac{3x^{2}-1}{2x^{3}+6x^{2}-5}\\)\n3) \\(\\lim_{x \\rightarrow 2} \\frac{x-2}{x^{2}+3x-1}\\)\n4) \\(\\lim_{x \\rightarrow 3} \\frac{x^{2}-2x+1}{x-3}\\)\n5) \\(\\lim_{x \\rightar... |
1,526 | [{"role": "user", "content": "In the coordinate plane, point $A$ is marked. Point $B$ is marked on the $Ox$ axis, and point $C$ is marked on the $Oy$ axis.\n\nIt is known that the equations of the lines $AB$, $BC$, and $AC$ in some order are $y=ax+4$, $y=2x+b$, and $y=\\frac{a}{2}x+8$ for some real numbers $a$ and $b$.... |
1,632 | [{"role": "user", "content": "If the line $y=kx+1$ intersects the circle $O: x^2+y^2=1$ at points $A$ and $B$, and $\\angle AOB=60^\\circ$, then the real number $k=$ \\_\\_\\_\\_\\_\\_ ."}, {"role": "assistant", "content": "<think>\n\nOkay, let's see. The problem is about a line intersecting a circle, and we need to fi... |
1,619 | [{"role": "user", "content": "Find the sum of the distinct prime factors of $7^7 - 7^3$."}, {"role": "assistant", "content": "<think>\n\nThis is a complex or challenging question, and it is difficult to provide a direct and correct answer. I need to think about it.\nWell, so I need to find the sum of the distinct prime... |
1,559 | [{"role": "user", "content": "Let $a$ and $b$ be real numbers. Define $f_{a,b}\\colon R^2\\to R^2$ by $f_{a,b}(x;y)=(a-by-x^2;x)$ . If $P=(x;y)\\in R^2$ , define $f^0_{a,b}(P) = P$ and $f^{k+1}_{a,b}(P)=f_{a,b}(f_{a,b}^k(P))$ for all nonnegative integers $k$ .\r\n\r\nThe set $per(a;b)$ of the *periodic p... |
1,664 | [{"role": "user", "content": "A company has a total of 1000 employees across various departments. A stratified sampling method is employed to draw a sample of 80 employees from the entire workforce. It is known that 4 employees were sampled from the advertising department. The number of employees in the advertising dep... |
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